1 / 10

5.3 Determining Sample Size to Estimate p

5.3 Determining Sample Size to Estimate p. To Estimate a Population Proportion p. If you desire a C% confidence interval for a population proportion p with an accuracy specified by you, how large does the sample size need to be?

roz
Download Presentation

5.3 Determining Sample Size to Estimate p

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. 5.3 Determining Sample Size to Estimate p

  2. To Estimate a Population Proportion p • If you desire a C% confidence interval for a population proportion p with an accuracy specified by you, how large does the sample size need to be? • We will denote the accuracy by ME, which stands for Margin ofError.

  3. Required Sample Size n to Estimate a Population Proportion p

  4. Confidence level Sampling distribution of .95

  5. What About p and q=1-p?

  6. Example: Sample Size to Estimate a Population Proportion p • The U. S. Crime Commission wants to estimate p = the proportion of crimes in which firearms are used to within .02 with 90% confidence. Data from previous years shows that p is about .6

  7. Example: Sample Size to Estimate a Population Proportion p (cont.)

  8. Example: Sample Size to Estimate a Population Proportion p The Curdle Dairy Co. wants to estimate the proportion p of customers that will purchase its new broccoli-flavored ice cream. Curdle wants to be 90% confident that they have estimated p to within .03. How many customers should they sample?

  9. Example: Sample Size to Estimate a Population Proportion p (cont.) • The desired Margin of Error is ME = .03 • Curdle wants to be 90% confident, so z*=1.645; the required sample size is • Since the sample has not yet been taken, the sample proportion p is still unknown. • We proceed using either one of the following two methods:

  10. Example: Sample Size to Estimate a Population Proportion p (cont.) • Method 1: • There is no knowledge about the value of p • Let p = .5. This results in the largest possible n needed for a 90% confidence interval of the form • If the proportion does not equal .5, the actual ME will be narrower than .03 with the n obtained by the formula below. • Method 2: • There is some idea about the value of p (say p ~ .2) • Use the value of p to calculate the sample size

More Related